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Although educational technology improves learning in other areas, its effect on geometric proof has been limited. To address this gap, the work interviews 18 geometry teachers to define technical requirements, then reviews 33 commercial and research tools. Results show a mismatch: teachers use certain digital tools for planning and exploration but return to pen-and-paper for formal proof. A key missing capability is diagram annotation support within the proof workflow. The paper proposes four design guidelines focused on integrating diagrams and proofs, automating problem generation and feedback, supporting multiple proof formats, and reducing interface complexity.",{"@graph":69,"@context":122},[70,84,105],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":40,"@type":76,"position":81},"https://docshare.wps.com/document/research-report/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/teaching-geometric-proof-with-tech-pitfalls-and-possibilities/657578/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":99,"encodingFormat":97,"isAccessibleForFree":100,"interactionStatistic":101},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/teaching-geometric-proof-with-tech-pitfalls-and-possibilities/657578.png","ImageObject",300,407,{"name":92,"@type":93},"Bulrr","Person",{"url":74,"name":95,"@type":96},"DocShare","Organization","application/pdf","2026-10-30","2026-10-26",true,{"@type":102,"interactionType":103,"userInteractionCount":81},"InteractionCounter",{"@type":104},"ViewAction",{"@type":106,"mainEntity":107},"FAQPage",[108,114,118],{"name":109,"@type":110,"acceptedAnswer":111},"Why is geometric proof difficult for students to learn?","Question",{"text":112,"@type":113},"It requires integrating spatial understanding, logical reasoning, and symbolic or notational skills simultaneously.","Answer",{"name":115,"@type":110,"acceptedAnswer":116},"What gap does the research identify about technology use in geometric proof?",{"text":117,"@type":113},"Teachers value some digital tools for planning and exploration, but current tools do not adequately support the formal proof workflow, especially diagram annotation.",{"name":119,"@type":110,"acceptedAnswer":120},"What design guidelines are proposed for educational proof tools?",{"text":121,"@type":113},"The paper proposes four guidelines: integrate diagram and proof, generate problems and feedback automatically, support multiple proof formats, and reduce accidental complexity in the user experience.","https://schema.org",{"og:url":83,"og:type":124,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":126,"canonical":83},"index,follow",{"doc_id":128,"site_id":62},657578,1792983744,{"code":4,"msg":5,"data":131},{"doc_id":128,"user_id":132,"nickname":92,"user_avatar":133,"doc_module":4,"category_id":39,"category_name":40,"doc_title":65,"doc_description":67,"doc_content":134,"file_id":135,"file_url":136,"file_type":137,"file_size":138,"view_count":81,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":139,"language":140,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":141,"faqs":142,"seo_title":143,"seo_description":67,"update_tm":129,"read_time":144},5909892115043,"https://ap-avatar.wpscdn.com/davatar_6f874abed73319feea01a86fa6f0fab8","arXiv : 2608 .25 1 17v 1 [cs .HC] 25 Aug 2026  \nTeaching Geometric Proof with Tech: Pitfalls and Possibilities  \nHWEI-SHIN HARRIMAN, Carnegie Mellon University, USAWODE NI, Carnegie Mellon University, USA  \nYUCHEN JIN, University of Wisconsin-Madison, USA DOMINIK MORITZ, Carnegie Mellon University, USA JOSHUA SUNSHINE, Carnegie Mellon University, USA  \nGeometric proof is a foundational yet challenging topic in mathematics, requiring students to integrate visual, logical, and notational skills. While technology has enhanced learning in other mathematical domains, its impact on geometric proof remains limited. To investigate this gap, we interviewed 18 geometry teachers to establish the technical requirements of educational proof tools. These requirements inform our review of 33 commercial and research tools. Our findings reveal a critical mismatch: while teachers value certain digital tools for initial planning and exploration activities, they revert to pen-and-paper for formal proof because it supports diagram annotation and provides space for multiple approaches to proof-solving. Annotating the diagram is a key component of the proof-solving workflow that existing tools do not support. We propose four technical and human-centered design guidelines for educational proof tools to meet teacher needs at scale: integrating diagram and proof, generating problems and feedback automatically, supporting multiple proof formats, and reducing accidental complexity in the user experience.  \nAdditional Key Words and Phrases: Geometry, Proof, Education, Learning, K-12 Education, Interview, Tool Review, Math Education, Education Technology  \nACM Reference Format:  \nHwei-Shin Harriman, Wode Ni, Yuchen Jin, Dominik Moritz, and Joshua Sunshine. 2026. Teaching Geometric Proof with Tech: Pitfalls  \nand Possibilities. 1, 1 (August 2026), 33 pages. [https://doi.org/10.1145/nnnnnnn.nnnnnnn](https://doi.org/10.1145/nnnnnnn.nnnnnnn)  \n1 Introduction  \nProof is the heart of mathematics; it is the mechanism that transforms conjecture into established fact. Geometry traditionally serves as the primary entry point for formal deductive reasoning. Its inherent visual nature provides a tangible bridge between intuitive observation and abstract logic. Despite its importance, geometric proof remains oneof the most difficult topics for students to master, as it requires the simultaneous integration of spatial, logical, and symbolic skills [1–3] . To address these instructional challenges, many educators look toward digital tools. In other areas of mathematics, such as arithmetic or algebra, educational technology has successfully improved learning outcomes by offering immediate feedback, interactivity, and personalization [4] . However, these benefits have not translated to geometric proof with the same degree of success. We hypothesize that this discrepancy exists because proof instruction  \nAuthors’ Contact Information: Hwei-Shin Harriman, Carnegie Mellon University, Pittsburgh, PA, USA, [harriman@cmu.edu](harriman@cmu.edu); Wode Ni, Carnegie Mellon  \nUniversity, Pittsburgh, USA, [nimo@cmu.edu](nimo@cmu.edu); Yuchen Jin, University of Wisconsin-Madison, Madison, USA, [rainyjin2016@gmail.com](rainyjin2016@gmail.com); Dominik Moritz,  \nCarnegie Mellon University, Pittsburgh, USA, [domoritz@cmu.edu](domoritz@cmu.edu); Joshua Sunshine, Carnegie Mellon University, Pittsburgh, USA, [sunshine@cs.cmu.edu](sunshine@cs.cmu.edu).  \nPermission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than the author(s) must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, [requires prior specific permission and/or a fee. Request","cbCaiq4bgNiZ0mCh","https://ap.wps.com/l/cbCaiq4bgNiZ0mCh","pdf",1704302,33,"English","# Introduction\n## Teachers’ role and research questions (RQ1, RQ2)\n## Interview study and tool review approach","[{\"question\":\"Why is geometric proof difficult for students to learn?\",\"answer\":\"It requires integrating spatial understanding, logical reasoning, and symbolic or notational skills simultaneously.\"},{\"question\":\"What gap does the research identify about technology use in geometric proof?\",\"answer\":\"Teachers value some digital tools for planning and exploration, but current tools do not adequately support the formal proof workflow, especially diagram annotation.\"},{\"question\":\"What design guidelines are proposed for educational proof tools?\",\"answer\":\"The paper proposes four guidelines: integrate diagram and proof, generate problems and feedback automatically, support multiple proof formats, and reduce accidental complexity in the user experience.\"}]","Teaching Geometric Proof with Tech: Pitfalls and Possibilities | PDF",83]